Device and method for generating an arrangement of a set of particles

ABSTRACT

A simulation device calculates an equilibrium arrangement of a set of particles by using a potential function or a force function, which describes an interaction of a particle system, and simulates the particle system by using an obtained equilibrium arrangement as an initial arrangement.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a device and a method for generating the information representing the arrangement of a set of particles in a particle system simulation.

[0003] 2. Description of the Related Art

[0004] As one method for analyzing and predicting the nature of a material composed of an inorganic or an organic substance, a simulation based on an MD (Molecular Dynamics) calculation exists. To perform this calculation, the initial arrangement of atoms or molecules, which form the material, must be generated. In the MD calculation, attempts are made to solve a differential equation (a Newton equation, etc.) by using a given initial arrangement as an initial value, to examine the nature of the system representing the material with a calculation result, and further, to implement the prediction of the nature.

[0005] However, experimental data on the arrangement of a system of molecules (the positional coordinates of all of atoms forming molecules) is not obtained in many cases although experimental data on a molecule structure considered to be a stable state of one molecule or a density of mass of the molecules at normal temperature and pressure is obtained. Accordingly, it is not known how to generate the initial arrangement of the molecules, which realizes an experimentally obtained density of mass of the molecules, when the MD calculation of a molecule system is made.

[0006] Considered as a simple method for generating the initial arrangement of a set of particles in a unit cell is a method for calculating the number of particles per the cell from the experimental data on the density of mass of the particles, and for arranging particles in the cell at random. However, if the particles are arranged completely at random, a pair of particles which have a close distance is sometimes generated. It is known that very intense force is applied between the close particles.

[0007] If even one such pair of close particles exists, the velocity of the particles increase due to an interaction between them, so that the temperature of the system becomes very high locally in the neighborhood of the pair. Accordingly, a very large numerical value occurs when a differential equation is solved, which sometimes leads to a failure of a numerical value integral algorithm.

[0008] As conventional methods for preventing such a simulation failure, the following three methods can be deviced. Normally, these methods are combined and used in many cases.

[0009] (1) Heat Emission Method

[0010] This is a method for emitting heat of a system generated during a simulation at suitable timing. Specifically, the velocity of each particle is decreased or reduced to “O”.

[0011] (2) Potential Relaxation Method

[0012] This is a method for preventing very intense force from being applied between close particles by weakening an interaction with the transformation of a potential function in a region where a distance between particles is short. With this method, the form of the potential function is continually changed during simulation, and is restored to its original function form by degrees. At this time, if all of the distances between respective particles are (equal to or) larger than a predetermined value R_(i) as a result of the measurement of the distances between particles, the potential function is restored to the original function form. The value of R_(i) is input as a parameter beforehand.

[0013] (3) Cell Size Change Method

[0014] This is a method for starting simulation after setting a cell whose size is larger than a size calculated from the experimental data on a density of mass of the particles. With such a cell, the probability that a pair of particles which have a close distance is generated becomes small even if particles are arranged at random. At this time, if a pair of particles, whose distance is smaller than a predetermined value R_(d), is found as a result of the measurement of the distances between particles, the particles are rearranged at random. Such a trial is iterated, and a normal simulation is started when all of the distances between particles become (equal to or) larger than R_(d).

[0015] However, the above described conventional simulation methods have the following problems.

[0016] (1) Heat Emission Method

[0017] If a given initial arrangement happens to be an arrangement which does not cause a failure of a numerical integral algorithm, a simulation can properly work. However, there is no such guarantee. Thus, this method must be combined with any of the other methods.

[0018] Additionally, if heat emission timing is unsuitable, the simulation cannot properly work. If the timing is delayed, the numerical integral algorithm encounters a failure, or numerical errors are accumulated, which can possibly cause a failure. On the contrary, if heat is emitted too often, the velocity of respective particles slow down, so that time development of the system change becomes slow, which leads to a high calculation cost.

[0019] (2) Potential Relaxation Method

[0020] It is not easy to set parameters (such as a parameter for specifying transformation timing, and a parameter for specifying a transformed function form), and know-how is required. Although an empirically determined setting may be sometimes available, the simulation cannot properly work depending on a target system. Trial and error for setting parameters is required in many cases.

[0021] Additionally, these parameters must be set for each pair of atom types so as to effectively set them. However, this setting operation becomes complex if a system is complicated.

[0022] Furthermore, it is important that also a determination condition for restoring a potential function should be suitably set. When a “go” determination for restoring a potential function to its original form is made before entering a fully equilibrium state, an extra calculation cost can possibly be incurred.

[0023] To explain this, we show the simulation result shown in FIG. 1A which is obtained as a result of combining the heat emission and the potential relaxation methods, applying to a system of alkane molecules. In FIG. 1A, the horizontal axis represents a time (different from a calculation time) describing a physical change in a system, “U” represents the value (gA²fs⁻²) of a potential function (internal energy), “V” represents the volume (A³) of a cell, and “T” represents a temperature (K).

[0024] In this example, a “go” determination is made in the neighborhood of 0.6×10⁻¹ ps. However, since its timing is unsuitable, intense force is applied between particles after the “go” determination is made. As a result, the volume “V” of the cell is expanded. Therefore, a considerable calculation cost is required until the volume “V” approaches the value based on experimental data.

[0025] Additionally, if an interaction is not a 2-body force, the operation for transforming a potential function is difficult to be formulated.

[0026] (3) Cell Size Change Method

[0027] If a cell size is not sufficiently large, the number of times that the trial of a random arrangement for generating an initial arrangement is iterated increases, which leads to complicatedness. However, if the cell size is too large, a lot of time is taken to restore the cell to its original size by means of experimental data. In a system where an interaction is complicated and the number of particles is large like a system of macromolecules, the cost of the restoration is high. It may be sometimes necessary to make a calculation for several hours in a supercomputer until a density of mass of the molecules calculated from a cell size approaches experimental data.

[0028] Suppose that the simulation result shown in FIG. 1B is obtained as a result of applying the cell size change method to a system of 20 liquid crystal molecules. In FIG. 1B, the time represented by the horizontal axis and “U”, “V”, and “T” are the same as those shown in FIG. 1A. In this example, a calculation is required to be made for many hours until the volume “V” converges.

[0029] As described above, it cannot be said that the method (1) through (3) are truly satisfactory methods from an easy-to-use, general-purpose, or a calculation cost viewpoint. Therefore, an easy-to-use and highly general-purpose simulation method which never causes an algorithm failure due to a huge numerical value and requires a low calculation cost is desired.

SUMMARY OF THE INVENTION

[0030] An object of the present invention is to provide a device and a method for generating an initial arrangement of a set of particles, which improves a particle system simulation process.

[0031] In a first aspect of the present invention, a generating device comprises a calculating unit and an outputting unit, and generates a set of particles arrangement in a particle system simulation. The calculating unit calculates an equilibrium arrangement of a set of particles in an arbitrarily dimensional space, while the outputting unit outputs an obtained equilibrium arrangement as an initial arrangement in the simulation.

[0032] In a second aspect of the present invention, a simulation device comprises a calculating unit, a simulating unit, and an outputting unit. The calculating unit calculates an equilibrium arrangement of a set of particles in an arbitrarily dimensional space. The simulating unit performs a particle system simulation by using an obtained equilibrium arrangement as an initial arrangement. The outputting unit outputs a simulation result.

BRIEF DESCRIPTION OF THE DRAWINGS

[0033]FIG. 1A shows a first conventional simulation result;

[0034]FIG. 1B shows a second conventional simulation result;

[0035]FIG. 2 shows the principle of a generating device according to the present invention;

[0036]FIG. 3 shows input data;

[0037]FIG. 4A is a flowchart showing the process for generating an equilibrium arrangement (No. 1);

[0038]FIG. 4B is a flowchart showing the process for generating an equilibrium arrangement (No. 2);

[0039]FIG. 5 shows a pseudo-random arrangement;

[0040]FIG. 6 shows a first equilibrium arrangement;

[0041]FIG. 7 shows a random arrangement;

[0042]FIG. 8 shows a second equilibrium arrangement;

[0043]FIG. 9 shows a potential change;

[0044]FIG. 10 is a block diagram showing the configuration of an information processing device; and

[0045]FIG. 11 shows storage media.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0046] Explained below are the details of preferred embodiments according to the present invention, by referring to the drawings.

[0047]FIG. 2 shows the principle of a generating device according to the present invention. A generating device shown in FIG. 2 comprises a calculating unit 1 and an outputting unit 2, and generates a set of particles arrangement in a particle system simulation. The calculating unit 1 calculates an equilibrium arrangement of a set of particles in an arbitrarily dimensional space, while the outputting unit 2 outputs an obtained equilibrium arrangement as an initial arrangement.

[0048] The equilibrium arrangement of a set of particles corresponds to an arrangement where interactions acting on respective particles are sufficiently small. This arrangement can be obtained, for example, from a potential function or a force function, which describes a particle system interaction. The calculating unit 1 calculates the equilibrium arrangement of the set of particles in a given dimensional space, while the outputting unit 2 outputs the equilibrium arrangement as the initial arrangement to a simulation program, etc.

[0049] Since an arrangement is displaced, for example, by a predetermined amount during the generation of an equilibrium arrangement in such a generating device, the displacement operation is different from the conventional operation based on the acceleration and the velocity of a particle. Accordingly, there is no need to worry about an algorithm failure occurring due to a huge numerical value, which is caused by the acceleration and the velocity of a particle. Therefore, it is unnecessary to use the conventional heat emission method, the potential relaxation method, and the cell size change method in a simulation, thereby reducing a calculation cost required by these methods. To be more specific, a velocity calculation required for a dynamics and a thermal calculation, a timing determination and an emission process calculation in the heat emission method, a parameter adjustment calculation in the potential relaxation method, and a cell size adjustment calculation in the cell size change method become unnecessary.

[0050] For example, the calculating unit 1 and the outputting unit 2, which are shown in FIG. 2, correspond to a CPU (Central Processing Unit) 21 and a memory 22, which will be described later and are shown in FIG. 10.

[0051] Additionally, a simulation device including such a generating device comprises a simulating unit for simulating a particle system by using the obtained equilibrium arrangement as the initial arrangement in addition to the calculating unit 1 and the outputting unit 2. In this case, the outputting unit 2 corresponds to an output device 24 shown in FIG. 10, and outputs a simulation result. Furthermore, the simulating unit corresponds to the CPU 21 and the memory 22, which are shown in FIG. 10.

[0052] As described above, the point of the present invention is to use an equilibrium arrangement of a set of particles as an initial arrangement in a simulation.

[0053] In this preferred embodiment, given particles are not arranged at random, but an equilibrium arrangement of a set of particles is obtained by considering an interaction between particles and an obtained equilibrium arrangement is adopted as an initial arrangement in a simulation.

[0054] Considered first is the case where an interaction between particles is given by a potential function. In this case, an equilibrium arrangement of a set of particles composed of “N” particles is represented as a state where a system potential function “U” takes a local minimum value. Here, “U” is defined by the following equation as a continuous function which has a subset “D” of R^(n) as a domain and takes a real number value.

[0055] U: R^(n)⊃D→R,

q=(q ₁ , . . . , q _(n))→U(q)  (1)

[0056] where “q” indicates an n-dimensional vector, and real numbers q₁, . . . q_(n) indicate “n” degrees of freedom. If a space where particles are arranged is assumed to be an m-dimensional space, n=Nm. The positional vectors r₁, . . . , r_(N) of the respective particles are represented by the following equations.

r₁≡(q₁n , . . . , q_(m)),

r₂≡(q_(m+1), . . . , q_(2m)),

. . .

r_(N)≡(q_((N−1)m+1), . . . q_(Nm))  (2)

[0057] Additionally, “U” can be decomposed for an arbitrary i(i=1, . . . , n) as indicated by the following equations.

U=U ^((i)) +{overscore (U)} ^((i)),  (3)

{overscore (U)} ^((i))(q ^((i)))−{overscore (U)} ^((i))(q)=0, for ∀aεD  (4)

[0058] Where q^((i)) is an n-dimensional vector defined by the following equation.

q^((i))≡(q₁, . . . , q_(i)+Δq_(i), . . . , q_(n))  (5)

[0059] The equation (4) represents that {overscore (U)}^((i)) (hereinafter denoted as U^((i)) bar) remains unchanged when q_(i) is changed by Δq_(i). In other words, U^((i)) bar in the equation (3) corresponds to a portion which does not depend on q_(i) of U, while U^((i)) corresponds to a portion which depends on q_(i) of U.

[0060] If U is represented by the sum of several of terms and includes a term which does not depend on q_(i), U^((i))=U−(U^((i)) bar) may be defined by setting this term to U^((i)) bar. In other cases, U^((i))≡U, and U^((i)) bar≡0 may be set. For example, a potential function of 2-body force, which is frequently used in simulations, is represented by the sum of potential functions φ between two particles by the following equation. $\begin{matrix} {{U(q)} = {\sum\limits_{1 \leq {i\quad j} \leq N}{\varphi \quad \left( {{r_{i} - r_{j}}} \right)}}} & (6) \end{matrix}$

[0061] In this case, U^((i)) is given by the following equation. $\begin{matrix} {{U^{(i)}(q)} = {\sum\limits_{j = {1{({j \neq i})}}}^{N}{\varphi \left( {{r_{i} - r_{j}}} \right)}}} & (7) \end{matrix}$

[0062] Now the relationship represented by the following expression is generally satisfied between U and U^((i)).

U(q ^((i)))<U(q)

U ^((i))(q ^((i)))<U ^((i))(q)  (8)

[0063] Accordingly, q may be changed to decrease U^((i)), so that U becomes small. By repeating such operations, the positions of respective particles, which correspond to the local minimum value of U can be obtained with ease.

[0064] Next, an algorithm of such an equilibrium arrangement generation process is explained by referring to FIGS. 3 through 4B.

[0065]FIG. 3 shows input data. In this input data, a degree of freedom 11 represents the number n of state variables q_(i) describing a given problem, initial coordinates 12 of particles represent the initial positions of N particles in an m-dimensional space.

[0066] Additionally, descent method conditions 13 include the number of steps, the width of a micro-displacement, a termination condition, an output specification parameter, etc. The number of steps represents the number of times that the descent method is iterated. The width of a micro-displacement represents an amount of displacement of the variable q_(i). The termination condition represents a termination condition of the descent method. The output specification parameter is a parameter for specifying an output interval of data to be output, etc. As the termination condition, for example, the following conditions are used.

[0067] (a) The iteration process is terminated when a calculation time or the number of processed steps reaches a predetermined value.

[0068] (b) The iteration process is terminated when a change in the potential U(q) becomes smaller than a predetermined determination value.

[0069] Additionally, a boundary condition 14 represents a boundary condition for the domain “D” of the potential function. For example, if a torus is specified as the boundary condition, a calculation is made by regarding the area “D” as torus (i.e., periodic boundary condition).

[0070] Furthermore, a cut-off length 15 is a parameter for simplifying an interaction. To increase a calculation efficiency, an interaction apart by the distance corresponding to the cut-off length 15 or more can be ignored as an optional capability.

[0071]FIGS. 4A and 4B are flowcharts showing an equilibrium arrangement generation process performed by the generating device according to the this preferred embodiment. The generating device first sets input data like the one shown in FIG. 3 (step S1 of FIG. 4A). At this time, an input data setting method is inquired to a user (step S2), and the data is automatically generated with a predetermined method (step S3), or the data is read from a predetermined external file (step S4) according to a user selection.

[0072] Here, n is input as the degree of freedom 11, and the number of iteration times, n micro-displacement sizes Δ1, Δ2, . . . , Δn, and a convergence determination parameter ε (>0) are input as the descent method conditions 13. Although respectively different values are normally used as the micro-displacement sizes Δ1, Δ2, . . . , Δn, the same value may be used as these sizes.

[0073] Next, the control variable “i” of the degree of freedom is set to “1” (step S5). The boundary condition process for the potential function is performed (step S6). Then, the processes in steps S7, S8, and S9 are performed. In step S7, the value of U^((i))(q₁, . . . , q_(n)) in the equation (3) is calculated, and an obtained value is set as U(i)0.

[0074] In step S8, the value of q_(i) corresponding to an i-th degree of freedom is micro-displaced in a positive direction, and set as “qi+”. Then, the value of U(q₁, . . . , q_(n)) is calculated by using qi+, and an obtained value is set as “U(i)+”. In step S9, the value of q_(i) is micro-displayed in a negative direction, and set as “qi−”. Then, the value of U(q₁, . . . , q_(n)) is calculated by using qi−, and an obtained value is set as “U(i)−”. qi+ and qi− are generated by an arbitrary calculation using Δi. For the simplest calculation, qi+=q_(i)+Δi, qi−=q_(i)−Δi may be set.

[0075] Next, the values of U(i)0, U(i)+, and U(i)− are compared (step S10 of FIG. 4B). If U(i)0 is the smallest, q_(i) is adopted as a new value of q_(i). In this case, the value of q_(i) remains unchanged. If U(i)+ is the smallest, qi+ is adopted as a new value of q_(i). If U(i)− is the smallest, qi− is adopted as a new value of q_(i).

[0076] Next, i=i+1 is set (step S11), and i is compared with n (step S12). If i does not exceed n, the processes in and after step S6 of FIG. 4A are repeated. Such processes are repeated for i=1, 2, . . . , n, so that the micro-displacement for all of the degrees of freedom are made.

[0077] If i exceeds n in step S12, it is then determined whether or not a predetermined termination condition is satisfied (step S13). If the termination condition is determined not to be satisfied, the descent method process in and after step S5 of FIG. 4A is repeated. When the termination condition is determined to be satisfied, the descent method process is terminated (step S14), q₁, . . . , q_(n), U⁽¹⁾(q₁, . . . , q_(n)), . . . , U^((n))(q₁, . . . , q_(n)), and U(q₁, . . . , q_(n)) at that time are output as output data (step S15). Here, the process is terminated.

[0078] Considered as the termination condition in step S13 is, for example, a condition that a suitable convergence condition for a change in the potential function is satisfied, or a condition that the descent method is terminated when the number of iteration times reaches an input number of times. As the convergence condition, for example, the condition represented by the following expression using a convergence determination parameter ε is utilized.

|U ^((i))(q ₁ , . . . , q _(n))−U(i)0|/|U(i)0|<ε  (9)

[0079] for i=1, . . . , n

[0080] Furthermore, in step S15, the positions of N particles are made visible on a display screen by using the obtained q₁, . . . , q_(n), and the equilibrium arrangement of the N particles is displayed. The data q₁, . . . , q_(n) representing the equilibrium arrangement is used as initial arrangement data in a MD simulation, etc.

[0081] Here, the same Δi is used in each iteration of the descent method. However, Δi may be changed each time the descent method is iterated. Additionally, various conditions can be used as a convergence condition other than the condition represented by the expression (9).

[0082] With such an algorithm, parameters such as the number of times that the descent method is iterated, the convergence condition, and the like can be set with ease, which eliminates the need for making a complicated parameter setting as required in the conventional potential relaxation method. Accordingly, no particular know-how is demanded, so that an equilibrium arrangement can be generated with ease.

[0083] Considered next is the case where the interaction between particles is given by the force function (a continuous function) represented by the following expression.

[0084] F: R^(n)⊃D→R^(n),

q=(q ₁ , . . . , q _(n))→F(q)  (10)

[0085] where F(q) represents an n-dimensional force vector. In this case, an equilibrium arrangement of N particles is given by an n-dimensional vector q by which F(q) becomes equal to “0”. Accordingly, a function “U” is defined by the following equation with the use of a continuous and strictly monotone increasing function “g”.

U(q ₁ , . . . , q _(n))=g(∥F(q ₁ , . . . . , q _(n))∥)  (11 )

[0086] Then, U is handled similar to the potential function U represented by the equation (3), and the state where its local minimum value is realized is obtained. The positions of respective particles in the obtained state correspond to an equilibrium arrangement. Generally, the case where an interaction is given by a force function includes the case where the interaction is given by a potential function, which is considered to be applicable to a lot more problems.

[0087] As described above, according to this preferred embodiment, also interactions (such as an N-body interaction, an interaction given by a force function, etc.) can be handled in a general-purpose manner in addition to the 2-body interaction represented by the equation (6).

[0088] Explained next is a specific example of the case where an interaction is given by a potential function. Assume that the potential function is given by the equation (6), and φ in the equation (6) is given by the following equation in a simulation of 100 argon atoms in a two-dimensional space (on a plane).

φ(r)=ε((σ/r)¹²−(σ/r)⁶)  (12)

[0089] Here, ε and σ are positive real numbers, and set as parameters. In this case, an equilibrium arrangement is generated with the above described algorithm by setting m=2, N=100, and n=200.

[0090]FIG. 5 shows a result obtained by slightly shifting 100 argon atoms from the positions of square lattices (pseudo-random) on an X-Y plane. As a result of calculating an equilibrium arrangement with the algorithm shown in FIGS. 4A and 4B starting from this arrangement, the arrangement shown in FIG. 6 is obtained. In this figure, something like a lattice defect is observed in some places. However, the arrangement analogous to an experimentally acquired FCC (Face Centered Cubic) structure is obtained.

[0091] Additionally, suppose that the argon atoms are arranged in a more random manner than in the arrangement shown in FIG. 5, for example, the arrangement shown in FIG. 7 is given. In this case, pairs of very close atoms are generated. Therefore, if a dynamics simulation is performed by using this arrangement as an initial arrangement, a temperature becomes locally high, which leads to an overflow occurrence.

[0092] As a result of calculating an equilibrium arrangement with the algorithm shown in FIGS. 4A and 4B starting from this arrangement, the arrangement shown in FIG. 8 is obtained. In FIG. 8, an arrangement analogous to the experimentally acquired structure is obtained in the same manner as in FIG. 6. At this time, the value of the potential function varies as shown in FIG. 9. It is known from FIG. 9 that the value of the potential function monotonically decreases with the iteration of the descent method calculation.

[0093] In the above described preferred embodiments, an equilibrium arrangement is obtained with the relatively simple descent method. Alternatively, a search method such as simulated annealing, a genetic algorithm, etc. may be used. Furthermore, as disclosed by the prior application “Processing Device and Method for Solving an Optimization Problem” (Japanese Patent Application No. 11-16500), an equilibrium arrangement may be obtained by using an algorithm searching for a low-cost shape while transforming a shape model representing an optimization problem. In this case, particles are used as transformation elements forming the shape model.

[0094] Additionally, a set of particles to be simulated is not limited to atoms or molecules. The present invention can be applied to a simulation of an arbitrary set of particles for which an interaction is predefined.

[0095] Furthermore, the space where particles are arranged is not limited to a two-dimensional space. The present invention can be applied to a simulation of a set of particles in an arbitrarily dimensional space. Normally, a simulation is performed in a three-dimensional space in many cases.

[0096] The above described generating device can be configured by using an information processing device (computer) shown in FIG. 10. The information processing device shown in FIG. 10 comprises a CPU (Central Processing Unit) 21, a memory 22, an input device 23, an output device 24, an external storage device 25, a medium driving device 26, and a network connecting device 27, which are interconnected by a bus 28.

[0097] The memory 22 includes, for example, a ROM (Read Only Memory), a RAM (Random Access Memory), etc., and stores the program and data used for processes. The CPU 21 performs necessary processes by executing the program with the memory 22.

[0098] The input device 23 is, for example, a keyboard, a pointing device, a touch panel, etc., and is used to input an instruction or information from a user. The output device 24 is, for example, a display, a printer, a speaker, etc., and is used to make an inquiry to a user or to output a process result.

[0099] The external storage device 25 is, for example, a magnetic disk device, an optical disk device, a magneto-optical disk device, etc. The information processing device stores the above described program and data onto the external storage device 25, and can use the program and data by loading them into the memory 22 depending on need. Additionally, the external storage device 25 is also used as a database for storing input data files.

[0100] The medium driving device 26 drives a portable storage medium 29, and accesses its recorded contents. As the portable storage medium 29, an arbitrary computer-readable storage medium such as a memory card, a floppy disk, a CD-ROM (Compact Disc-Read Only Memory), an optical disk, a magneto-optical disc, etc. is used. A user stores the above described program and data in the portable storage medium 29, and can use the program and data by loading them into the memory 22 depending on need.

[0101] The network connecting device 27 communicates with an external device via an arbitrary network (line) such as a LAN (Local Area Network), etc., and performs data conversion accompanying a communication. The information processing device receives the above described program and data from the external device via the network connecting device 27, and can use the program and data by loading them into the memory 22 depending on need.

[0102] Furthermore, the simulation device simulating a particle system by using an equilibrium arrangement as an initial arrangement includes the above described generating device, and can be configured by an information processing device similar to that shown in FIG. 10. In this case, the CPU 21 performs a simulation process for MD, etc. by executing the program with the memory 22.

[0103]FIG. 11 shows computer-readable storage media which can provide a program and data to the information processing device shown in FIG. 10. The program and data stored onto the portable storage medium 29 or in an external database 30 are loaded into the memory 22. The CPU 22 then executes the program by using the data, and performs necessary processes.

[0104] According to the present invention, there is no need to consider the velocity of particles as conventional, and to worry about an algorithm failure due to a huge numerical value. Accordingly, it is unnecessary to use the conventional heat emission method, the potential relaxation method, and the cell size change method, which leads to a reduction in a calculation cost required for these method and an improvement in simulation operability. Furthermore, various interactions can be handled in a general-purpose manner. 

What is claimed is:
 1. A generating device for generating an arrangement of a set of particles in a particle system simulation, comprising: a calculating unit calculating an equilibrium arrangement of the set of particles in an arbitrarily dimensional space; and an outputting unit outputting an obtained equilibrium arrangement as an initial arrangement in the simulation.
 2. The generating device according to claim 1, wherein when an interaction of the particle system is described by a potential function, said calculating unit calculates the equilibrium arrangement by using the potential function.
 3. The generating device according to claim 1, wherein when an interaction of the particle system is described by a force function, said calculating unit calculates the equilibrium arrangement by using the force function.
 4. The generating device according to claim 3, wherein said calculating unit generates a potential function by using the force function, and calculates the equilibrium arrangement by using the potential function.
 5. A simulation device, comprising: a calculating unit calculating an equilibrium arrangement of a set of particles in an arbitrarily dimensional space; and a simulating unit performing a particle system simulation by using an obtained equilibrium arrangement as an initial arrangement; and an outputting unit outputting a result of the simulation.
 6. A generating device for generating an arrangement of a set of particles in a particle system simulation, comprising: calculating means for calculating an equilibrium arrangement of the set of particles in an arbitrarily dimensional space; and outputting means for outputting an obtained equilibrium arrangement as an initial arrangement in the simulation.
 7. A simulation device, comprising: calculating means for calculating an equilibrium arrangement of a set of particles in an arbitrarily dimensional space; and simulating means for performing a particle system simulation by using an obtained equilibrium arrangement as an initial arrangement; and outputting means for outputting a result of the simulation.
 8. A computer-readable storage medium on which is recorded a program for causing a computer to execute a process generating an arrangement of a set of particles in a particle system simulation, said process comprising: calculating an equilibrium arrangement of the set of particles in an arbitrarily dimensional space; and outputting an obtained equilibrium arrangement as an initial arrangement in the simulation.
 9. A simulation method, comprising: calculating an equilibrium arrangement of a set of particles in an arbitrarily dimensional space; and performing a particle system simulation by using an obtained equilibrium arrangement as an initial arrangement. 